The decomposition of MM tensors consists of optimizing a large number of parameters. The number of parameters can be reduced by utilizing special symmetries of the tensors. The tensors are symmetric and we can restrict our attention to symmetric decompositions only [1]}, [2]}. The issue of symmetric decomposition exceeds the scope of this paper. Here we present only the cyclic symmetry mentioned in [3]}, because we need it in our examples.
The symmetry holds for multiplying two square matrices, \(P=Q=S=N\) . This tensor is invariant to cyclic permutation of its indices. In Matlab notation, it holds that
\({\cal T}_{NNN}=permute({\cal T}_{NNN},[2,3,1])=permute({\cal T}_{NNN},[3,1,2]) .\) 
